1. Numbers (numerals: Duodecimal System)

1-4-5. Duodecimal is another system of numerals in which the base is twelve. Compared to 10, 12 has more factors so it can be divided more easily, besides it can be counted by fingers: excluding thumb, we have four fingers, each is divided into 3 parts or consists of 3 finger bones; so we can count up to 12. We can use the thumb moving over other fingers to count the amount.

We need to define two symbols for ten and eleven. Either A and B, or T and E is used to represent ten and eleven accordingly. Furthermore, a rotated 2 (ᘔ) and a reversed 3 (Ɛ) are proposed by Sir Isaac Pitman as symbols for ten and eleven respectively.

Duodecimal is also called dozenal system. That’s why we have a pack of dozen or half dozen products especially drinks. Now we can see why 13 is considered as an unlucky number. The 13^th product, let’s say can of drink, can ruin the divisibility of 12, moreover 13 is a prime number (it doesn’t have any factors but 1 and itself) which will be discussed later. So imagine you wanted to share 12 cans of drink between six friends, and now you had 13 cans, what would you do? Then the mythologies have amplified the unlucky power of 13.

That’s also why the words eleven and twelve are different from teen numbers. They stemmed from the Deutsche words elf and zwölf respectively.

In order to compare different numeral systems, we need to know the fractions and index form (that’s why I try to introduce them briefly), therefore, all different bases will be discussed elaborately after the history of numerals will have been discussed up to Hindu-Arabic numerals that we use these days. We will try to develop all arithmetic operations based on different bases, then we can compare their efficiency and drawbacks.